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Article or Presentation
99
views
27
downloads
0
comments
2002-Patrick_Nelson-Alan_Perelson-Mathematical_analysis_of_delay_differential _equation_models_of_HIV-1_infection
Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays.
delay
HIV-1
T cells
combination antiviral therapy
Potential Scenario
92
views
85
downloads
0
comments
2015-Jonathon_Easton, Jonathan-Mathematical models of health focusing on diabetes-Delay differential equations and data mining
This is an exhaustive study with very good references of a linear system of four differential equations with and without delay to model diabetes in a human being.
diabetes
health model
Potential Scenario
152
views
43
downloads
0
comments
2002-Nelson-Perelson-Mathematical analysis of delay differential equations models of HIV-1 infection
We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells.
infection
HIV
T cells
Potential Scenario
156
views
55
downloads
0
comments
1977-Michael_Mackey-Leon_Glass-Oscillation and Chaos in Physiological Control Systems
First-order nonlinear differential-delay equations describing physiological control systems are studied. The equations display a broad diversity of dynamical behavior including limit cycle oscillation.
sensitivity
chaos
parameters
Respiration
delay
blood cells
Potential Scenario
114
views
51
downloads
0
comments
2016-Barbarossa-Kuttler-Mathematical Modeling of Bacteria Communication in Continuous Cultures
This paper presents a simple system of delay differential equations (DDEs) for quorum sensing of Pseudomonas putida with one positive feedback plus one (delayed) negative feedback mechanism.
gene regulatory networks
chemostat
bifurcation
Numerical Simulation
quorum sensing
Potential Scenario
113
views
31
downloads
0
comments
1984-W_Brunner-D__Focht-Deterministic Three-Half-Order Kinetic Model for Microbial Degradation
The kinetics of mineralization of carbonaceous substrates has been explained by a deterministic model which is applicable to either growth or nongrowth conditions in soil.
kinetics
nonlinear regression
sum of square errors
Monodlinearize
mineralization
substrates
carbonaceous
Technique Narrative
308
views
116
downloads
0
comments
1-009-Bifurcation-TechniqueNarrative
We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.
bifurcation
qualitative behavior
bifurcation diagram
Potential Scenario
97
views
37
downloads
0
comments
2009-Marten-EtAl-Derivation and analysis of an ordinary differential equation for epilepsy dynamics
In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations.
delay
epilepsy dynamics
epilepsy
bistability
seizure activity
Potential Scenario
127
views
34
downloads
0
comments
2011-Kurt_Kreith-The Mathematics of Global Change
The authors discuss broad issues and then focus on specifics like exponential growth, logistic growth, and the logistic equation with delay.
exponential growth
logistic growth
Potential Scenario
146
views
37
downloads
0
comments
1969-Israelsson-Johnsson-Phase-shift in Geotropic Oscillations a Theoretical and Experimental Study
The paper studies geotropical induced phase-shifts in circumnutations (turning) of Helianthus annus hypocotlys.
plant
oscillation
delay
circumnutation
turning
Potential Scenario
263
views
56
downloads
0
comments
2017-Suebcharoen-Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator
This paper studies the behavior of a predator-prey model with switching and stage-structure for predator.
stage structure
predator
prey
bifurcation
switching
Potential Scenario
1561
views
45
downloads
0
comments
2018-Kovacs-Insperger-Retarded neutral and advanced differential equation models for balancing using an accelerometer
It is shown that slight modeling differences lead to significant qualitative change in the behavior of the system, which is demonstrated by means of the stability diagrams for the different models.
feedback
Accelerometers
functional differential equations
semi-discretization
D-subdivision method
Potential Scenario
110
views
61
downloads
0
comments
2017-Allali-EtAl-Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection
The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies.
logistic
HBV infection
adaptive immunie response
T-lymphocytes
Potential Scenario
141
views
68
downloads
0
comments
2015-Boggess-EtAl-Mathematical Modeling in Ecology - Simulating the Reintroduction of the Extinct Passenger Pigeon
To determine under which conditions a Passenger Pigeon could survive a reintroduction into a natural habitat, we used two types of models.
simulation
agent-based modeling
allee_effect
Passenger Pigeons
forest envirnoment
Holling Type III functional response
Bio-energetics
tree distributions
Potential Scenario
112
views
38
downloads
0
comments
2013-Greer-EtAl-Collaborative Understanding of Cyanobacteria in Lake Ecosystems
We describe here a collaboration in which the mathematicians help collect data, the ecologists synthesize more data from model output than they can produce empirically, and the collaboration produces both mathematical approaches and field work.
collaboration
lake
ecosystem
cyanobacteria
field work
colony
Gloeo
Potential Scenario
126
views
67
downloads
0
comments
2014-Rogert_Smith-Mathematical Modeling of Zombies
Here, we use diffusion to model the zombie population shuffling randomly over a one-dimensional domain.
kinetics
Zombie
zombification
interaction times
Potential Scenario
132
views
46
downloads
0
comments
2011-Yanyu_Xiao-Study of Malaria Transmission Dynamics by Mathematical Models
The novelty lies in the fact that different distribution functions are used to describe the variance of individual latencies. The theoretical results of this project indicate that latencies reduce the basic reproduction number.
infectious disease
infection
malaria
latency
spatial dispersal
multi-species
Modeling Scenario
365
views
272
downloads
0
comments
1-061-PotatoCooling-ModelingScenario
We model the cooling of a baked potato and compare it to student-collected data.
least sum of square errors
Newton's Law of Cooling
cooling
potato
Article or Presentation
99
views
42
downloads
0
comments
2011-Carl_Leinbach-Beyond_Newton_law_of_cooling_estimation_of_time_since_death
The estimate of the time since death. Thus, the time of death is strictly that, an estimate. However, the time of death can be an important piece of information in some coroner’s cases, especially those that involve criminal or insurance...
Newton's Law of Cooling
time of death
double exponential
coroner
Modeling Scenario
346
views
225
downloads
0
comments
5-076-LanchesterLaws-ModelingScenario
Lanchester's laws are used to calculate the relative strengths of military forces. The Lanchester equations are differential equations describing the time dependence of two armies' strengths A and B as a function of time,
Lanchester's laws
sensitivity analysisanalysis
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